Efficiently compiling a quantum circuit such as Eq. (REF ) to a real quantum processors, having pre-defined calibrated two-qubit gates active on a sparse subset of all possible pairs of qubits, is a non-trivial planning and scheduling problem [1]}. We would like to estimate the advantage of using QAMPA versus QAOA in common implementation scenarios. For \(\mathtt {WeightedMaxCutGSP}\) , the required \(U_{ZZ}\)  gates to implement the objective function are the \(N (N - 1) / 2\)  edges of a fully-connected graph. The mixer that is responsible for the exploration step of the algorithm by keeping the constraint (REF ) in check is also ideally a complete mixer, since it is proven numerically to be the best choice for Hamming weight constraints [2]}, [3]}, [4]}. Sparser choices for mixing graphs might lead to shorter circuits, but the compilation advantage of using QAMPA versus QAOA is maximal if we use the same graph for both phase-separation and mixing operations.
